On enhanced binding and related effects in the non- and semi-relativistic Pauli-Fierz models

TL;DR

This paper proves enhanced binding energies and improved localization of ground states in non- and semi-relativistic Pauli-Fierz models, analyzing effects of the fine-structure constant and ultra-violet cut-off, and exploring mass renormalization and self-energy asymptotics.

Contribution

It establishes enhanced binding and localization effects in Pauli-Fierz models for all coupling strengths and cut-offs, including mass renormalization and self-energy asymptotics.

Findings

Enhanced binding energies proven for all coupling values.

Exponential localization of ground states improved.

Asymptotic behavior of self-energy analyzed as cut-off increases.

Abstract

We prove enhanced binding and increase of binding energies in the non- and semi-relativistic Pauli-Fierz models, for arbitrary values of the fine-structure constant and the ultra-violet cut-off, and discuss the resulting improvement of exponential localization of ground state eigenvectors. For the semi-relativistic model we also discuss the increase of the renormalized electron mass and determine the linear leading order term in the asymptotics of the self-energy, as the ultra-violet cut-off goes to infinity.